Shadow mapping over an illuminated terrain is an inherent part of topographic relief shading techniques. Unless blocked from the light source, a given grid point on a surface is subject to a direct beam radiance defined by a local normal to the surface at the given grid point and local slope and aspect angles, which can be estimated using as small a local area as a 3×3 pixel kernel around the given grid point.
Preliminary Definitions: As used herein, and in any appended claims, the following terms shall have the meanings indicated, unless the context dictates otherwise:                The term “shadowing,” or, synonymously, “shadow mapping,” “shadow casting,” or “shadow projection,” as used herein, shall denote adding shadows to a three-dimensional image of a scene. A particular example includes the generation of a radiance map (as defined below) of incident or reflected light energy as a blocking mask (as the term is defined below) for a direct beam radiance component of total insolation energy flux. However, it is to be understood that the scope of the invention encompasses shadowing, whether or not a blocking mask is produced.        A “map” is a function (finite, but not necessarily continuous) assigning a value to each point in a domain.        The term “radiance map” shall denote a map assigning a value (which may have units, or not) to each point of a terrestrial area, associated with whether light from a specified source reaches that point.        A “blocking mask” is a radiance map that assumes one of two binary values, indicating whether light from a specified source reaches each point of a terrestrial area or not.        The term “insolation energy flux” refers either to watt-hours per square meter for a specified duration of time, or to instantaneous watts per square meter (i.e., a insolation power flux) incident at a specified terrestrial point due to irradiation by a specified source, typically the Sun, whether directly or due to scattering or reflection. The component of the insolation energy flux that is due to direct illumination of a point is called the “direct beam radiance component of the total insolation energy flux.”        The term “slope” shall refer to the magnitude (the modulus) of the gradient of elevation taken at a local point.        The term “aspect angle” shall refer to the direction in which the gradient of elevation at a local point is maximal, defined with respect to a specified fiducial direction, typically north.        The term “sky view” shall mean the line of sight along a ray from a specified point to effectively infinity in a specified direction.        A “viewshed” shall mean the sky view in all directions relative to a specified point, which is to say, all surrounding points that are in line-of-sight (LOS) with the specified point.        The term “light vector” denotes a direction in space from a given point to the position of a source of illumination, as defined by the centroid of its brightness profile. “Brightness” and other photometric terms are as defined in Lang, Astrophysical Formulae (1980). The source of illumination is effectively at infinite distance from an anchor point, which is to say that the wavefront of light emanating from the source of illumination is effectively normal to all rays emanating from the source of illumination and incident upon the anchor point (defined below). The direction associated with a light vector may be specified in azimuth-elevation (AZ-EL) coordinates, or in accordance with any other system of coordinates. It is to be understood that the same term “light vector” applies, in equal measure, to a ray oriented along the same line but in the opposite direction, namely from the source of illumination to a specified anchor point.        The term “sun vector” denotes a light vector associated with the Sun. The term may be used heuristically herein for convenience of description, and may readily be generalized by a reader of ordinary skill in the art to encompass the Moon, or other illumination sources, natural or artificial.        The given point with respect to which directions (such as the aforementioned “light vector” or “sun vector”) are determined is referred to herein as the “anchor point.”        
In areas of complex topography, geometry mandates that one must know the sky view in all directions for a point in order to determine if a given sun vector (specified, for example, in coordinates of (azimuth, elevation), referred to, herein, also as (AZ, EL)) is in view from that point, or not. Techniques to compute viewshed for a topographic point as a polar plot of radial coordinate for elevation and tangential coordinate for azimuth are designed in the paper by J. Tovar-Pescador et al., “On the use of the digital elevation model to estimate the solar radiation in areas of complex topography”, Meteorol. Appl., vol. 13, 279-287 (2006). A schematic process to generate point-based viewshed maps designed by J. Tovar-Pescador et al. is shown in FIGS. 1A-1C. FIG. 1A shows a digital elevation model (DEM) of a scene centered about a specified grid point 101. FIG. 1B is an elevation cross section of the skyview relative to grid point 101, while FIG. 1C is an azimuth-elevation (AZ-EL) representation of the viewshed relative to grid point 101.
In addition to the absence of full 3D geometric data, another daunting feature of GIS data sets is the very large quantity of data that must be processed, often in a near real-time mode. The initial process to generate a viewshed for each point is computationally very expensive; however, the following shadow map generation for any given time of day (or intervals of time) is very fast. The accuracy limitation of the method is defined by a discrete number of azimuth directions selected to generate a viewshed profile in polar coordinates: interpolating between just 12 directions is obviously of lower fidelity than, say, 360 directions.